If I drop something and a baby picks it up and hands it to me how to say thank you.  Is it kob khun, kob jai or kob chai?

I often hear adults around me with children say the full "kob khun khrap" extra slowly and clearly as a way to be an example of how to be polite.

KhobChai certainly will do the job.

Thats too what I say when paying my Taxi fare to signal the driver he does not need to return the change

Babies don’t speak so it doesn’t matter what you say provided it is sincere. Your own language would do.

If the child is walking and able to talk I call them หนู,  say ขอบใจ  and use จ๊ะ instead of ครับ . 

Rightly or wrongly, I think that I about to find out! ขอบใจจ๊ะหนู 

Thais generally use 'thank you' less than most native English speakers would do at home, particularly the British perhaps. So you generally wouldn't need to say anything like that to a child. Though I think ubonrthai has picked up on something that Thais often do to teach their kids. 
Saying 'khob chai' to a taxi driver doesn't really show much awareness of the language. 

Actually i wanted to write: ขอบใจ (kawp jai) is Lao or Isaan, why would you say this unless you are in Laos?

But then i looked it up and saw that according to the thai-language.com it is indeed also Thai and would match: to thank someone with lower rank or status (e.g. one's younger brothers or sisters or one's students)

But i did never hear Bangkok people say ขอบใจ

From what i've learned by living in Bangkok: To say ขอบคุณครับ (kawp khun krap) is never wrong, for both adults and children. But if you consider this too polite or just too long to say you can just say "kraaaap" (just stretch the word) in a friendly way.

Probably most people have heard "you can never be overdressed or overeducated". In my opinion you can add "you can never be too polite" to this

 

We have been taught from Thai school that you have to use whether "Khob KHun" or Khob Jai"  according to your and the 2nd party hierarchical status but nowaday I feel weird when somebody saying "Khob Jai"  and thinking Khob Khun must be the best all around. For this case , just add Krab ครับ or Kha ค่ะ  according to gender of that kid (not the speaker) is appropriate enough.

I myself hardly say either Khob KHun or Khob Jai among my family. It's too formal for me  and I don't want to กระแดะพูด. 

I have been greeted by ladies of a passing aquaintance of my own age on the course with ครับ and of course wonder if they see it as helping a me out as they would a child.